Problem: Igor the analyst has adopted n little bunnies. As we all know, bunnies love carrots. Thus, Igor has bought a carrot to be shared between his bunnies. Igor wants to treat all the bunnies equally, and thus he wants to cut the carrot into n pieces of equal area. 

Formally, the carrot can be viewed as an isosceles triangle with base length equal to 1 and height equal to h. Igor wants to make n - 1 cuts parallel to the base to cut the carrot into n pieces. He wants to make sure that all n pieces have the same area. Can you help Igor determine where to cut the carrot so that each piece have equal area?

<image> Illustration to the first example.

Input

The first and only line of input contains two space-separated integers, n and h (2 ≤ n ≤ 1000, 1 ≤ h ≤ 105).

Output

The output should contain n - 1 real numbers x1, x2, ..., xn - 1. The number xi denotes that the i-th cut must be made xi units away from the apex of the carrot. In addition, 0 < x1 < x2 < ... < xn - 1 < h must hold. 

Your output will be considered correct if absolute or relative error of every number in your output doesn't exceed 10 - 6.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if <image>.

Examples

Input

3 2


Output

1.154700538379 1.632993161855


Input

2 100000


Output

70710.678118654752

Note

Definition of isosceles triangle: <https://en.wikipedia.org/wiki/Isosceles_triangle>.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class B{
	static int N;
	static double h, botAngle, topAngle;
	
	public static void main(String[] args) {
		FastScannerB sc = new FastScannerB(System.in);
		
		N = sc.nextInt();
		h = sc.nextInt();
		
		double area = (double)(1*(double)h)/2.0;
		
		
		double side = Math.sqrt(h*h + 0.5*0.5);
		
//		System.out.println(side);
		
		topAngle = (Math.asin(0.5/side));
		
		botAngle = Math.toRadians(90) - topAngle;
		topAngle *= 2;
		
//		area /= Math.sin(Math.toRadians(botAngle));
		
		double piece = area/N;
		
//		System.out.println(area + " piece = " + piece);
		
		ArrayList<Double> list = new ArrayList<>();
		
		for(int i = 0 ; i < N-1 ; i++){
			double val = binSearch(area - piece, h);
			list.add(val);
			h = val;
			area -= piece;
		}
		Collections.sort(list);
		
		for(int i = 0 ; i < N-1 ; i++){
			System.out.print(list.get(i) + " ");
		}
		
		
//		System.out.println(botAngle + " " + topAngle);
//		
//		System.out.println(area);
//		System.out.println(side*Math.sin(Math.toRadians(botAngle))/2);
	}

	public static double binSearch(double left, double r){
		
//		double leftSide = (2 * left)/Math.sin(Math.toRadians(botAngle));
//		leftSide *= 2;
		
//		System.out.println("calculating piece between 0 and " + r + " height for area = " + left );
		
		double l = 0.0;
		int turns = 0;
		
		while(Math.abs(r-l) > 0.000000001 && l < r && turns < 500){
			turns++;
			
			double mid = l + (r - l) / 2;
//			System.out.println("L = " + l + " R = " + r + "  Mid = " + mid);
			
			double bot = calculateBot(left, mid);

//			System.out.println("bot = " + bot + " Bot Angle = " + botAngle);
			if(bot < botAngle){
				l = mid;
			}//70710.6781184848
			else if(bot > botAngle){
				r = mid;
			}
			else{
//				double lBot = calculateBot(left, l);
//				double rBot = calculateBot(left, r);
//				if(lBot == rBot || lBot == bot){
//					r = mid;
//				}
//				else{
//					l = mid;
//				}
//				
				l = mid;
			}
			
//			System.out.println("Updated to L = " + l + " R = " + r);
			
//			double temph = Math.sqrt((leftSide - mid*mid*mid*mid) / mid*mid);
			
//			if(temph )
		}
//		System.out.println("Returning result = " + (l + (r-l)/2));
		return (l + (r-l)/2);
	}

	private static double calculateBot(double left, double mid) {
		double tempa = 2*left/mid;
		
		double side = Math.sqrt(mid*mid + tempa*tempa/4);
		
		double top = (Math.asin((tempa/2)/side));
		
		double bot = Math.toRadians(90) - top;
		return bot;
	}
	
}

class FastScannerB{
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public FastScannerB(InputStream stream)
    {
        this.stream = stream;
    }

    public int read()
    {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars)
        {
            curChar = 0;
            try
            {
                numChars = stream.read(buf);
            } catch (IOException e)
            {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int nextInt()
    {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-')
        {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do
        {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String next()
    {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do
        {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }
    
    public String nextLine()
    {
        int c = read();
        StringBuilder res = new StringBuilder();
        do
        {
            res.appendCodePoint(c);
            c = read();
        } while (!isLineEndChar(c));
        return res.toString();
    }    
    
    public double nextDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E')
                return res * Math.pow(10, nextInt());
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }
    
    public long nextLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
    
    public boolean isSpaceChar(int c)
    {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
    
    public boolean isLineEndChar(int c)
    {
        if (filter != null)
            return filter.isSpaceChar(c);
        return c == '\n' || c == '\r' || c == -1;
    }

    public interface SpaceCharFilter
    {
        public boolean isSpaceChar(int ch);
    }
}